Question

- Show that E(x,t) = Emax. Cos (kx – wt)

And B(x,t) = Bmax. Cos (kx – wt)

Are solutions to the Wave Equations

Answer #1

A common solution to the wave equation is E(x,t) = A ei(kx+wt).
On paper take the needed derivatives and show that it actually is a
solution. Note that i is the square-root of -1. Upload a photograph
of your work.

Show that x(t) = A sin(wt) sin(kx) satisfies the wave equation,
where w and k are some constants. Find the relation between w, k,
and v so that the wave equation is satisfied.

Show numerically that, if a wave cos kx centred on A
(so that x is measured from A) interferes with a similar
wave cos k′x centred on B (with x
measured from B) a distance R away, then constructive
interference occurs in the intermediate region when k =
k′ = π/2R and destructive interference if
kR= 1/2π and k′R= 3/2π

A standing wave’s function is y(x,t) = Asin(kx)cos(?t). Prove
that this equation is indeed a solution to the wave equation.

A sound wave of the form s = sm cos(kx - ?t + f) travels at 343
m/s through air in a long horizontal tube. At one instant, air
molecule A at x = 2.000 m is at its maximum positive displacement
of 6.00 nm and air molecule B at x = 2.070 m is at a positive
displacement of 2.00 nm. All the molecules between A and B are at
intermediate displacements. What is the frequency of the wave?

If v(t) = 5 cos(wt+60°) V & i(t) = 4 cos(wt) A, What is the expression for instataneous power?

An electromagnetic wave in a medium is given by the following
wave function expression:
E=5E0(i-2j)sin(kx-wt).
The wave is known to have a wavelength of 690 nm and frequency of
3.2*1014 Hz. Also E0=104 V/m. For
this wave find the propagation number, angular frequency, direction
of propagation, speed of wave, index of refraction of medium,
direction of E oscillation, direction of
corresponding B oscillation, amplitude of
E, amplitude of B, and calculate
the irradiance of this wave.

Show that the curve
x = 7 cos(t), y = 6 sin(t) cos(t)
has two tangents at (0, 0) and find their equations.

Determine whether cos ( k x ) e x p ( − i ω t ) is
an acceptable solution to the time-dependent Schrödinger wave
equation.

a plane electromagnetic sinusoidal wave propagating in the x
direction. Suppose the wavelength is 48.0 m and the electric field
vibrates in the xy plane with an amplitude of 20.0 V/m.
(a) Calculate the frequency of the wave.__________ MHz
(b) Calculate the magnetic field B when the electric field has
its maximum value in the negative y direction. magnitude
__________nT
(c) Write an expression for B with the correct unit vector, with
numerical values for Bmax, k, and ω,
and...

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